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Home , Grote Reber

Fundamentals of James Miller-Jones (NRAO Charlottesville/Curtin University)

ITN 215212: Black Hole Universe Many slides taken from NRAO Synthesis Imaging Workshop (http://www.aoc.nrao.edu/events/synthesis/2010/) and the radio astronomy course of J. Condon and S. Ransom Atacama Large Millimeter/ (http://www.cv.nrao.edu/course/astr534/ERA.shtml) Expanded Robert C. Byrd What is radio astronomy?

• The study of radio waves originating from outside the Earth • Wavelength range 10 MHz – 1 THz • Long wavelengths, low frequencies, low photon energies – Low-energy transitions (21cm line) – Cold astronomical sources – Stimulated emission (masers) – Long-lived synchrotron emission • Sources typically powered by gravity rather than nuclear fusion – Radio galaxies – Supernovae – Pulsars – X-ray binaries

2nd School on Multiwavelength Astronomy, Amsterdam , June 2010 2 What is radio astronomy?

• Telescope resolution q = 1.02 l/D – Requires huge dishes for angular resolution • Coherent (phase preserving) amplifiers practical

– Quantum noise proportional to frequency T = hn/kB • Precision telescopes can be built s

2nd School on Multiwavelength Astronomy, Amsterdam , June 2010 3 A short historical digression

• Extraterrestrial radio signals first detected in 1932 by Karl – Electrical engineer working for – Attempting to determine origin of radio static at 20.5 MHz – Steady hiss modulated with a period 23h 56min – Strongest towards the Galactic Centre • Discovery ignored by most astronomers, pursued by Grote Reber – 1937-1940: Mapped the Galaxy at 160 MHz – Demonstrated the spectrum was non-thermal • World War II stimulated rapid progress in radio and radar technology

2nd School on Multiwavelength Astronomy, Amsterdam , June 2010 4 Why radio astronomy?

• Atmosphere absorbs most of the EM spectrum – Only optical and radio bands accessible to ground-based instruments • Rayleigh scattering by atmospheric dust prevents daytime optical • Radio opacity from water vapour line, hydrosols, molecular oxygen – High, dry sites best at high frequencies • Stars undetectably faint as thermal radio sources – Non-thermal radiation – Cold gas emission – CMB 2hn 3 1 2k Tn 2 B T    B  0.3Jy n c2 hn c2 e kBT 1

2nd School on Multiwavelength Astronomy, Amsterdam , June 2010 5 A tour of the radio Universe

2nd School on Multiwavelength Astronomy, Amsterdam , June 2010 6 What are we looking at?

• Synchrotron radiation – Energetic charged particles accelerating along magnetic field lines (non-thermal)

• What can we learn? • particle energy

• strength of magnetic field

• polarization

• orientation of magnetic field

2nd School on Multiwavelength Astronomy, Amsterdam , June 2010 7 What are we looking at?

• Thermal emission – Blackbody radiation from cool (T~3-30K) objects – Bremsstrahlung “free-free” radiation: charged particles interacting in a plasma at T; e- accelerated by ion • H II regions • What can we learn? • mass of ionized gas

• optical depth

• density of electrons in plasma

• rate of ionizing photons

2nd School on Multiwavelength Astronomy, Amsterdam , June 2010 8 What are we looking at?

• How to distinguish continuum mechanisms?  • Look at the spectrum

Spectral index across a SNR Flux or Flux Density Density Flux or Flux Frequency 

 • Spectral index From T. Delaney Sn n

2nd School on Multiwavelength Astronomy, Amsterdam , June 2010 9 What are we looking at?

• Spectral line emission (discrete transitions of atoms and molecules) – Spin-flip 21-cm line of HI – Recombination lines – Molecular rotational/vibrational modes • What can we learn? • gas physical conditions

• kinematics (Doppler effect)

2nd School on Multiwavelength Astronomy, Amsterdam , June 2010 10 The Sun

• Brightest discrete radio source • Atmospheric dust doesn‟t scatter radio waves

Image courtesy of NRAO/AUI

2nd School on Multiwavelength Astronomy, Amsterdam , June 2010 11 The planets

• Thermal emitters • No reflected solar radiation detected • Jupiter is a non-thermal emitter (B field traps electrons) • Also active experiments: radar

Jupiter Mars (radar) Saturn

Images courtesy of NRAO/AUI

2nd School on Multiwavelength Astronomy, Amsterdam , June 2010 12 Stars

• Coronal loop resolved in the Algol system • Tidally-locked system, rapid rotation drives magnetic dynamo

Credit: Peterson, Mutel, Guedel, Goss (2010, Nature)

2nd School on Multiwavelength Astronomy, Amsterdam , June 2010 13 Black holes and neutron stars

Blundell & Bowler (2004)

Mirabel & Rodriguez (1994) Dhawan et al. (2000)

Dhawan et al. (2006) Gallo et al. (2005) Dubner et al. (1998)

2nd School on Multiwavelength Astronomy, Amsterdam , June 2010 14 Center of our Galaxy VLA 20cm

VLA 1.3cm

VLA 3.6cm 1 LY

SgrA* - 4 milliion Mo black hole source15 Credits: Lang, Morris, Roberts, Yusef-Zadeh, Goss, Zhao Radio Spectral Lines: Gas in galaxies

2nd School on Multiwavelength Astronomy, Amsterdam , June 2010 16 Jet Energy via Radio Bubbles in Hot Cluster Gas

1.4 GHz VLA contours over Chandra X-ray image (left) and optical (right) 6 X 1061 ergs ~ 3 X 107 solar masses X c2 (McNamara et al. 2005, Nature, 433, 45)

17 Resolution and Surface-brightness Sensitivity

18 The Cosmic Microwave Background

• 2.73 K radiation from z~1100 • Angular power spectrum of brightness fluctuations constrains cosmological parameters

2nd School on Multiwavelength Astronomy, Amsterdam , June 2010 19 Definitions

2 In (or Bn ) = Surface Brightness : erg/s/cm /Hz/sr (= intensity) S = Flux density : erg/s/cm 2/Hz I  n  n S = Flux : erg/s/cm 2 I n  n P = Power received : erg/s I nA  n tel E = Energy : erg I nA t  n tel

2nd School on Multiwavelength Astronomy, Amsterdam , June 2010 20 Radio astronomy: instrumentation

• Antennas convert electromagnetic radiation into electrical currents in conductors • Average collecting area of any lossless Prime focus Cassegrain antenna (GMRT) l2 (ATCA) A  e 4

– Long wavelength: dipoles sufficient – Short wavelength: use reflectors to Offset cassegrain Naysmith collect and focus power from a large (EVLA) (OVRO) area onto a single feed • Parabola focuses a plane wave to a single focal point Dual offset Beam waveguide offset (NRO) (GBT)

2nd School on Multiwavelength Astronomy, Amsterdam , June 2010 21 Types of antennas

• Wire antennas (l 1m) – Dipole – Yagi – Helix – Small arrays of the above • Reflector antennas (l 1m) • Hybrid antennas – Wire reflectors (l 1m) – Reflectors with dipole feeds

2nd School on Multiwavelength Astronomy, Amsterdam , June 2010 22 Fundamental antenna equations

P(q,,n)  A(q,,n )I(q,,n)n • Effective collecting area A(qn) m2 • On-axis response

Ao=hA • Normalized pattern (primary beam)

A(qn) = A(qn)/Ao • Beam solid angle

A= ∫∫ A(n,q,) d all sky

2 • AoA = l

2nd School on Multiwavelength Astronomy, Amsterdam , June 2010 23 Aperture-Beam Fourier Transform Relationship

• Aperture field distribution and far-field voltage pattern form FT relation

f l  g(u)e2iludu aperture • u = x/l • lsin q • Uniformly-illuminated aperture gives sinc function response qD  P(q)  sinc2    l  • qHPBW  l/D

2nd School on Multiwavelength Astronomy, Amsterdam , June 2010 24 Antenna efficiency

On axis response: A0 = hA Efficiency: h = hsf . hbl  hs  ht  hmisc rms error s hsf = Reflector surface efficiency Due to imperfections in reflector surface 2 hsf = exp[(4s/l) ] e.g., s = l/16 , hsf = 0.5 hbl = Blockage efficiency Caused by subreflector and its support structure

hs = Feed spillover efficiency Fraction of power radiated by feed intercepted by subreflector ht = Feed illumination efficiency Outer parts of reflector illuminated at lower level than inner part hmisc= Reflector diffraction, feed position phase errors, feed match and loss

2nd School on Multiwavelength Astronomy, Amsterdam , June 2010 25

• Largest fully-steerable dishes have D~100m – l/D ≤ 10-4 at cm wavelengths • Sub-arcsecond resolution impossible • Confusion limits sensitivity – Collecting area limited to D2/4 • Tracking accuracy limited to s~1” – Gravitational deformation – Differential heating – Wind torques – Must keep s < l/10D for accurate imaging/photometry • Interferometers consisting of multiple small dishes mitigate these problems

2nd School on Multiwavelength Astronomy, Amsterdam , June 2010 26 Interferometry

• Interferometry = – Combine signals from multiple small apertures – Technique developed in the 1950s in and Australia. – (University of Cambridge) earned a Nobel Prize for his contributions. • Basic operation: Correlation = multiply and average separate voltage outputs

2nd School on Multiwavelength Astronomy, Amsterdam , June 2010 27 Interferometry

• We seek a relation between the characteristics of the product of the voltages from two separated antennas and the distribution of the brightness of the originating source emission.

• To establish the basic relations, consider first the simplest interferometer: – Fixed in space – no rotation or motion – Quasi-monochromatic – Single frequency throughout – no frequency conversions – Single polarization (say, RCP). – No propagation distortions (no , atmosphere …) – Idealized electronics (perfectly linear, perfectly uniform in frequency and direction, perfectly identical for both elements, no added noise, …)

2nd School on Multiwavelength Astronomy, Amsterdam , June 2010 28 The two-element interferometer • Radiation reaching 1 is delayed relative to 2 • Output voltage of antenna 1 lags by geometric delay

tg = b.s/c • Multiply outputs:

2 V1V2 V cost cost t g  V 2  cos2t t  cost  2 g g

• Time-average the result V 2 R  VV  cost  1 2 2 g multiply average

2nd School on Multiwavelength Astronomy, Amsterdam , June 2010 29 The two-element interferometer

V 2 R  VV  cost  1 2 2 g • Sinusoidal variation with changing source direction: fringes bcosq   t  g c d  bsinq   2  dq  l 

• Fringe period l/bsinq • Phase measures source position (for large b)

2nd School on Multiwavelength Astronomy, Amsterdam , June 2010 30 The two-element interferometer

V 2 R  VV  cost  1 2 2 g • Sensitivity to a single Fourier component of sky brightness, of period l/bsinq

• Antennas are directional • Multiply correlator output by antenna response (primary beam)

2nd School on Multiwavelength Astronomy, Amsterdam , June 2010 31 Adding more elements • Treat as N(N-1)/2 independent two-element interferometers • Average responses over all pairs • Synthesized beam approaches a Gaussian • For unchanging sources, move antennas to make extra measurements

2nd School on Multiwavelength Astronomy, Amsterdam , June 2010 32 Extended sources V 2 • Point source response of our cosine correlator: R  VV  cost  1 2 2 g V 2  S A A 1/ 2 2 n 1 2 • Treat extended sources as the sum of individual point sources – Sum responses of each antenna over entire sky, multiply, then average R  V d V d c  1 1  2 2 * • If emission is spatially incoherent n R1 n R2   0 for R1  R2

• Then we can exchange the integrals and the time averaging  b.s  Rc  In scos2n d   c 

2nd School on Multiwavelength Astronomy, Amsterdam , June 2010 33 Odd and even brightness distributions  b.s  • Response of our cosine correlator: Rc  In scos2n d   c  • This is only sensitive to the even (inversion-symmetric) part of the

source brightness distribution I = IE+IO • Add a second correlator following a 90o phase shift to the output of one antenna V 2 R  VV  sint  s 1 2 2 g  b.s  Rs  In ssin2n d   c 

I IE IO = +

2nd School on Multiwavelength Astronomy, Amsterdam , June 2010 34 Complex correlators A = (R 2+R 2)1/2 • Define complex visibility V = R -iR = Aei c s c s  = tan-1(R /R ) • Thus response to extended source is s c

 b.s  Vn  In sexp 2i d   l  • Under certain circumstances, this is a Fourier transform, giving us a well established way to recover I(s) from V – 1) Confine measurements to a plane – 2) Limit radiation to a small patch of sky

• Use an interferometer to measure the spatial coherence function Vn and invert to measure the sky brightness distribution

2nd School on Multiwavelength Astronomy, Amsterdam , June 2010 35 Digression: co-ordinate systems

• Baseline b measured in wavelengths: the (u,v,w) co-ordinate system

– w points along reference direction so – (u,v) point east and north in plane normal to w-axis – (u,v,w) are the components of b/l along these directions

• In this co-ordinate system, s = (l,m,n) – l,m,n are direction cosines – n = cos q = (1-l2-m2)1/2

 b.s  V  I sexp 2i d n  n l dldm   d  I (l,m) 1l 2  m2 V u,v, w  n exp 2iul  vm wndldm n  2 2 1l  m

2nd School on Multiwavelength Astronomy, Amsterdam , June 2010 36 Measurements confined to a plane

• All baselines b lie in a plane, so b = r1-r2 = l(u,v,0) • Components of s are then l,m, 1l 2  m2  e2i(ulvm) V u,v, w  0  I (l,m) dldm n  n 2 2 1l  m • This is a Fourier-transform relationship between Vn and In, which we know how to invert 2 2 • Earth-rotation synthesis (so is Earth‟s rotation axis): 1l  m  cosq  sec – E-W interferometers – ATCA, WSRT • VLA snapshots

2nd School on Multiwavelength Astronomy, Amsterdam , June 2010 37 All sources in a small region of sky

• Radiation from a small part of celestial sphere: s = so+s • n = cos q = 1 – (q2/2) I (l,m) V u,v, w  e2iw n exp 2iul  vm wq 2 / 2dldm n  2 2 1l  m • If wq 2 << 1, i.e. q~(l/b)1/2 then we can ignore last term in brackets I (l,m) Vu,v, w  e2iw n e2i(ulvm)dldm n  2 2 1l  m 2iw • Let Vn u,v,w  e Vn(u,v,w) I (l,m) V u,v  n e2i(ulvm)dldm n  2 2 1l  m • Again, we have recovered a Fourier transform relation • Here the endpoints of the vectors s lie in a plane • Break up larger fields into multiple facets each satisfying wq 2 << 1

2nd School on Multiwavelength Astronomy, Amsterdam , June 2010 38 All sources in a small region of sky

• This assumption is valid since antennas are directional

V u,v  A (l,m)I (l,m)e2i(ulvm)dldm n    n n

• Primary beam of interferometer elements An gives sensitivity as a function of direction

• Falls rapidly to 0 away from pointing centre so • Holds where field of view is not too large – centimetre-wavelength interferometers • EVLA • MERLIN • VLBA • EVN • GMRT

2nd School on Multiwavelength Astronomy, Amsterdam , June 2010 39 Visibility functions

• Brightness and Visibility are Fourier pairs. • Some simple and illustrative examples make use of „delta functions‟ – sources of infinitely small extent, but finite total flux.

2nd School on Multiwavelength Astronomy, Amsterdam , June 2010 40 Visibility functions

• Top row: 1-dimensional even brightness distributions. • Bottom row: The corresponding real, even, visibility functions.

Inq

Vn(u)

2nd School on Multiwavelength Astronomy, Amsterdam , June 2010 41 Inverting the Fourier transform

• Fourier transform relation between measured visibilities and sky brightness I (l,m) V u,v  n e2i(ulvm)dldm n  2 2 1l  m

• Invert FT relation to recover sky brightness I l,m n  V (u,v)e2i(ulvm)dudv 2 2  n 1l  m • This assumes complete sampling of the (u,v) plane • Introduce sampling function S(u,v) I D l,m n  V (u,v)S (u,v)e2i(ulvm)dudv 2 2  n n 1l  m D • Must deconvolve to recover In : In  In  B • See Katherine Blundell‟s lecture for details

2nd School on Multiwavelength Astronomy, Amsterdam , June 2010 42 Seems simple?

• We have discovered a beautiful, invertible relation between the visibility measured by an interferometer and the sky brightness • BUT: • Between the source and the correlator lie: – Atmosphere – Man-made interference (RFI) – Instrumentation • The visibility function we measure is not the true visibility function • Therefore we rely on: – Editing: remove corrupted visibilities – Calibration: remove the effects of the atmosphere and instrumentation obs true * true Vij  Gij Vij  GiGj Vij

2nd School on Multiwavelength Astronomy, Amsterdam , June 2010 43 What about bandwidth? n • Practical instruments are not monochromatic G • Assume: – constant source brightness – constant interferometer n0 n response over the finite bandwidth, then:  1 n c n / 2  Vn  n  In (s)exp 2intg dv d   n c n / 2  • The integral of a rectangle function is a sinc function: V  I (s)sinc(nt )exp(2in t )d n  n g c g • Fringe amplitude is reduced by a sinc function envelope

• Attenuation is small for ntg<< 1, i.e. nq  qsn

2nd School on Multiwavelength Astronomy, Amsterdam , June 2010 44 What about bandwidth?

• For a square bandpass, the bandwidth attenuation reaches a null at an angle equal to the fringe separation divided by the fractional

bandwidth: nn0 • Depends only on baseline and bandwidth, not frequency

Fringe Attenuation function:  b n  sinc q   l n 

c sin q  bn

2nd School on Multiwavelength Astronomy, Amsterdam , June 2010 45 Delay tracking

• Fringe amplitude reduced by sinc function envelope • Eliminate the attenuation in any

one direction so by adding extra delay t0 = tg • Shifts the fringe attenuation

function across by sin q = ct0/b to centre on source of interest

• As Earth rotates, adjust t -1 continuously so | t0 - tg| < (n • nq  qsn • Away from this, bandwidth smearing: radial broadening • Convolve brightness with rectangle nqn

2nd School on Multiwavelength Astronomy, Amsterdam , June 2010 46 Field of view • Bandwidth smearing – Field of view limited by bandwidth smearing to

q  qsnn Source – Split bandwidth into many narrow channels to widen e FOV q • Time smearing NCP – Earth rotation should not move source by 1 synthesized l/D beam in correlator averaging time – Tangential broadening – q  Pq 2t where Interferometer Primary Beam s Fringe Separation Half Power P=86164s (sidereal day) l/b

2nd School on Multiwavelength Astronomy, Amsterdam , June 2010 47 What about polarization?

• All the above was derived for a scalar electric field (single polarization) • Electromagnetic radiation is a vector phenomenon: – EM waves are intrinsically polarized – monochromatic waves are fully polarized • Polarization state of radiation can tell us about: – the origin of the radiation • intrinsic polarization, orientation of generating B-field – the medium through which it traverses • propagation and scattering effects – unfortunately, also about the purity of our optics • you may be forced to observe polarization even if you do not want to!

2nd School on Multiwavelength Astronomy, Amsterdam , June 2010 48 The Polarization Ellipse • From Maxwell‟s equations E•B=0 (E and B perpendicular) – By convention, we consider the time behavior of the E-field in a fixed perpendicular plane, from the point of view of the receiver. k E  0 transverse wave

• For a monochromatic wave of frequency n, we write

Ex  Ax cos2nt x 

Ey  Ay cos2nt  y  – These two equations describe an ellipse in the (x-y) plane. • The ellipse is described fully by three parameters:

– AX, AY, and the phase difference,  = Y-X.

2nd School on Multiwavelength Astronomy, Amsterdam , June 2010 Elliptically Polarized Monochromatic Wave

The simplest description of wave polarization is in a Cartesian coordinate frame.

In general, three parameters are needed to describe the ellipse.

If the E-vector is rotating: – clockwise, wave is „Left Elliptically Polarized‟, – counterclockwise, is „Right Elliptically Polarized‟.

equivalent to 2 independent Ex and Ey oscillators

2nd School on Multiwavelength Astronomy, Amsterdam , June 2010 Polarization Ellipse Ellipticity and P.A. • A more natural description is in a frame (xh), rotated so the x-axis lies along the major axis of the ellipse. • The three parameters of the ellipse are then: Ah : the major axis length tan c  AxAh : the axial ratio  : the major axis p.a.

• The ellipticity c is signed: c > 0  REP c < 0  LEP

c = 0,90°  Linear (=0°,180°) c = ±45°  Circular (=±90°)

2nd School on Multiwavelength Astronomy, Amsterdam , June 2010 Circular Basis • We can decompose the E-field into a circular basis, rather than a (linear) Cartesian one:   E  AReR  ALeL

– where AR and AL are the amplitudes of two counter-rotating unit vectors, eR (rotating counter-clockwise), and eL (clockwise) – NOTE: R,L are obtained from X,Y by a phase shift • In terms of the linear basis vectors: 1 A  A2  A2  2A A sin R 2 X Y X Y XY 1 A  A2  A2  2A A sin L 2 X Y X Y XY

2nd School on Multiwavelength Astronomy, Amsterdam , June 2010 Circular Basis Example

• The black ellipse can be decomposed into an x- component of amplitude 2, and a y-component of amplitude 1 which lags by ¼ turn. • It can alternatively be decomposed into a counterclockwise rotating vector of length 1.5 (red), and a clockwise rotating vector of length 0.5 (blue).

2nd School on Multiwavelength Astronomy, Amsterdam , June 2010 Stokes parameters

• Stokes parameters I,Q,U,V – defined by George Stokes (1852) – scalar quantities independent of basis (XY, RL, etc.) – units of power (flux density when calibrated) – form complete description of wave polarization – Total intensity, 2 linear polarizations and a circular polarization 2 2 2 2 • I = EX + EY = ER + EL 2 2 • Q = I cos 2c cos 2y = EX - EY = 2 ER EL cos RL

• U = I cos 2c sin 2y = 2 EX EY cos XY = 2 ER EL sin RL 2 2 • V = I sin 2c = 2 EX EY sin XY = ER - EL • Only 3 independent parameters: – I2 = Q2 + U2 + V2 for fully-polarized emission – If not fully polarized, I2 > Q2 + U2 + V2

2nd School on Multiwavelength Astronomy, Amsterdam , June 2010 Stokes parameters • Linearly Polarized Radiation: V = 0 – Linearly polarized flux: P  Q2 U 2 – Q and U define the linear polarization position angle: tan2 U /Q – Signs of Q and U:

Q > 0 U > 0 U < 0 Q < 0 Q < 0 U > 0 U < 0 Q > 0

2nd School on Multiwavelength Astronomy, Amsterdam , June 2010 Polarization example

• VLA @ 8.4 GHz – Laing (1996) • Synchrotron radiation – relativistic plasma – jet from central “engine” – from pc to kpc scales – feeding >10kpc “lobes” • E-vectors – along core of jet – radial to jet at edge 3 kpc

2nd School on Multiwavelength Astronomy, Amsterdam , June 2010 Sensitivity • The radiometer equation for point source sensitivity:

2kBTsys s S  Aeff N(N 1)tintn

• Increase the sensitivity by: • Increasing the bandwidth • Increasing the integration time • Increasing the number of antennas • Increasing the size/efficiency of the antennas • Surface brightness sensitivity is MUCH worse • synthesized beam << beam size of single dish of same effective area

2nd School on Multiwavelength Astronomy, Amsterdam , June 2010 57 Summary: why should I use radio telescopes?

• Unparalleled resolution – Astrometry: positions, velocities, distances – High-resolution imaging • Unique probe – Radio waves not scattered by dust: probe inner Galaxy – Low-energy, long-lived non-thermal emission – Spectral lines probe physical conditions of gas • Signature of high-energy processes; link to X-ray emission • Exotic phenomena – Coherent emission (pulsar phenomenon) • New “Golden Age” – New telescopes opening up new parameter space

2nd School on Multiwavelength Astronomy, Amsterdam , June 2010 58 Radio Astronomy: A Golden Age! WSRT EVLA EVN LOFAR

GMRT

VLBA ATCA SKA?

ALMA

MeerKAT LBA ASKAP

2nd School on Multiwavelength Astronomy, Amsterdam , June 2010 59 Equations to take away

• Resolution of an interferometer l q  bmax • Field of view of an interferometer l q  D • Sensitivity of an interferometer

2kBTsys s S  Aeff N(N 1)tintn

• Relation between visibility and sky brightness I (l,m) V u,v  n e2i(ulvm)dldm n  2 2 1l  m

2nd School on Multiwavelength Astronomy, Amsterdam , June 2010 60